Thanks for your question. According to Jewish law, the custom has been for me to have their heads covered while at prayer. This law dates back to Talmudic times, when men traditionally had their heads covered at all times as a sign of reverence and humility to God. Women never had such an obligation, because women were exempted from positive time bound commandments, of which prayer is one. (Women would pray, but had no obligation to do so with a "minyan." In my synagogue (a Conservative one) many women choose to have their heads covered too while praying. In Orthodoxy, women (generally married ones) also cover their heads when at worship services. This is both a sign of reverence to God. A covered head would also provide a "shield" to a woman's hair, which to many men is an attraction.